-tbvh- I don't see Izaya as the jealous type because he's just too emotionally detached
-however there are some exceptions to this rule
-for example, if he finds someone becoming to comfortable around his s/o [as in physically touching them too much], I doubt he'd have any trouble at all showing them who you belong to. Perhaps he would even familiarize the unlucky guy's neck with his trusty pocket knife.
-it really depends on his mood
-it can go from "So what, she's just one of my humans idm-" to "(name)-chan is my-chan so f u c k o f f :) "
-if he does become jealous, it was be a good idea not to tease him, however
-because a word of warning, he won't stop himself from leaving a few of his own property marks on you-